Question

determine a distância do ponto p(5,-4) e a reta da equaçao 5×+2=0​

Answer 1

$\sf r:5x+2=0\implies r:5x+0y+2=0.$

$\therefore$

$\sf d(p,r)=\dfrac{|a_rx_p+b_ry_p+c_r|}{\sqrt{a_r^2+b_r^2}}$

$\sf d(p,r)=\dfrac{|5\cdot5+0\cdot(-\,4)+2|}{\sqrt{5^2+0^2}}$

$\sf d(p,r)=\dfrac{|25+0+2|}{\sqrt{25+0}}$

$\sf d(p,r)=\dfrac{|27|}{\sqrt{25}}$

$\red{\sf d(p,r)=\dfrac{27}{5}\,un.}$